# Isomorphism of weighted trees and Stanley's conjecture for caterpillars.

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Martin Loebl, Charles U., Prague
Fine Hall 224

We show that the U-polynomial distinguishes non-isomorphic caterpillars.

This settles a longstanding special case of Stanley's conjecture and the Noble, Welsh conjecture (that the same is true for all trees).

Joint work with Jean-Sébastien Sereni.